Yes. If you have him subdued and the threat is neutralized you've done your part, now let the authorities handle the rest. It's not up to you whether he dies or not. You've successfully defended your home and that's all that matters. Let him rot in a jail cell. I'd say it's a lot more satisfying knowing you thwarted off this piece of shit and handed him over to the police. Then you can be like "Hey, got a present for ya!" when the cops show up. Then you can all laugh at the shithead while he sits in the back of the cop car.
However I'd say it'd be a different story if he broke in to your home armed with a gun. Then you have every right to do what you got to do to defend yourself and if you have a family them to. If he dies then he dies.